exp neg sub

Average Error: 0.0 → 0.0

Time: 1.8s

Precision: binary64

Math

\[e^{-\left(1 - x \cdot x\right)}\]

↓

\[e^{-1} \cdot {\left(e^{x}\right)}^{x}\]

Error

Bits error versus x

Derivation

1. Initial program 0.0

   \[e^{-\left(1 - x \cdot x\right)}\]
2. Using strategy rm

3. Applied sub-neg 0.0

   \[\leadsto e^{-\color{blue}{\left(1 + \left(-x \cdot x\right)\right)}}\]

4. Applied distribute-neg-in 0.0

   \[\leadsto e^{\color{blue}{\left(-1\right) + \left(-\left(-x \cdot x\right)\right)}}\]

5. Applied exp-sum 0.0

   \[\leadsto \color{blue}{e^{-1} \cdot e^{-\left(-x \cdot x\right)}}\]

6. Simplified 0.0

   \[\leadsto e^{-1} \cdot \color{blue}{e^{{x}^{2}}}\]
7. Using strategy rm

8. Applied unpow2 0.0

   \[\leadsto e^{-1} \cdot e^{\color{blue}{x \cdot x}}\]

9. Applied exp-prod 0.0

   \[\leadsto e^{-1} \cdot \color{blue}{{\left(e^{x}\right)}^{x}}\]

10. Final simplification 0.0

    \[\leadsto e^{-1} \cdot {\left(e^{x}\right)}^{x}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "exp neg sub"
  :precision binary64
  (exp (neg (- 1.0 (* x x)))))